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In this paper, we study a two-species reaction-diffusion-advection competition model imposed the Danckwerts boundary conditions and with boundary protection zones. Some special cases have been extensively studied, which include reaction-diffusion-advection competition models without protection zones [25,29] and reaction-diffusion competition models with protection zones in non-advective environments [7]. If the product of the two competition rates in the unprotected zone is less than a given value, by establishing a prior estimate and applying the monotone dynamical system theory, we completely characterize the global dynamics, which extends some existing ones. If the product is bigger than the above mentioned value, we find that the size of the protection zone plays an important role in determining the global dynamics. We also discuss the problem of optimal protection zone setting and investigate the effect of advection on the critical size of the protection zone. [ABSTRACT FROM AUTHOR]

Mandarin Chinese is typologically unusual among the world's languages in having flexible word order despite a near absence of inflectional morphology. These features of Mandarin challenge conventional linguistic notions such as subject and object and the divide between syntax and semantics. In the present study, we tested monolingual processing of argument structure in Mandarin verb-final sentences, where word order alone is not a reliable cue. We collected participants' responses to a forced agent-assignment task while measuring their electroencephalography data to capture real-time processing throughout each sentence. We found that sentence interpretation was not informed by word order in the absence of other cues, and while the coverbs BA and BEI were strong signals for agent selection, comprehension was a result of multiple cues. These results challenge previous reports of a linear ranking of cue strength. Event-related potentials showed that BA and BEI impacted participants' processing even before the verb was read and that role reversal anomalies elicited an N400 effect without a subsequent semantic P600. This study demonstrates that Mandarin sentence comprehension requires online interaction among cues in a language-specific manner, consistent with models that predict crosslinguistic differences in core sentence processing mechanisms. [ABSTRACT FROM AUTHOR]

This paper is concerned with the spreading behavior of a two-species strong-weak competition system with two free boundaries. The model may describe how a strong competing species invades into the habitat of a native weak competing species. The asymptotic spreading speed of invading fronts has been determined by making use of semi-wave systems in Du et al. (J Math Pures Appl 107:253–287, 2017). Here we give a sharp estimate for the asymptotic spreading speed of invading fronts. Moreover, we prove that the solution of the free boundary problem evolves eventually into a semi-wave solution when the spreading happens, while the solution of the free boundary problem exponentially converges to a semi-trivial solution of such system when the vanishing happens. [ABSTRACT FROM AUTHOR]

In this paper, we incorporate stoichiometry into a competition model in chemostat culture. We first discuss the dynamics of this stoichiometric chemostat model for single algae species. We obtain the uniform persistence and find that an increase of phosphorus input or a slow dilution rate facilitates the algal persistence. Then, we consider a stoichiometric chemostat model in which two species competing for single nutrient, investigate how stoichiometry, dilution rate and concentration of phosphorus input affect the result of competition between algae species. Competitive exclusion and coexistence of two competing algae species are explored by discussing the existence, local stability of all feasible equilibria. Previous studies suggested that competitive exclusion holds in general chemostat models with two species competing for one limiting nutrient. Our theoretical and numerical results demonstrate that stoichiometry brings the coexistence of two competing algae species. Moreover, under low phosphorus input or fast dilution rate, competitive exclusion still holds. High phosphorus input or slow dilution rate facilitates the coexistence of multiple species. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Chongqing University of Technology (Natural Science) is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract Mandarin Chinese is typologically unusual among the world’s languages in having flexible word order despite a near absence of inflectional morphology. These features of Mandarin challenge conventional linguistic notions such as subject and object and the divide between syntax and semantics. In the present study, we tested monolingual processing of argument structure in Mandarin verb-final sentences, where word order alone is not a reliable cue. We collected participants’ responses to a forced agent-assignment task while measuring their electroencephalography data to capture real-time processing throughout each sentence. We found that sentence interpretation was not informed by word order in the absence of other cues, and while the coverbs BA and BEI were strong signals for agent selection, comprehension was a result of multiple cues. These results challenge previous reports of a linear ranking of cue strength. Event-related potentials showed that BA and BEI impacted participants’ processing even before the verb was read and that role reversal anomalies elicited an N400 effect without a subsequent semantic P600. This study demonstrates that Mandarin sentence comprehension requires online interaction among cues in a language-specific manner, consistent with models that predict crosslinguistic differences in core sentence processing mechanisms.

In this work, we propose and study a two species Lotka–Volterra competition model, where the first species experiences the mate-finding Allee effect caused by the second species. First, we study the presence and stability of all conceivable positive equilibria and boundary equilibria of this system. Next, by utilizing the Sotomayor theorem, we demonstrate that, given appropriate parameter circumstances, both a saddle-node bifurcation and a transcritical bifurcation exist. Finally, numerical simulations were carried out to validate our theoretical results further. We found that under certain conditions, the system appears to be bistable when the trait-mediated indirect effect is low. However, when the trait-mediated indirect effect is too high, the bistability of the system disappears, and the first species eventually tends to extinction. [ABSTRACT FROM AUTHOR]

A wide range of approaches has been used to manage the spread of invasive species, yet invaders continue to be a challenge to control. In some cases, management actions have no effect or may even inadvertently benefit the targeted invader. Here, we use the mid‐20th century management of the Red Imported Fire Ant, Solenopsis invicta, in the US as a motivating case study to explore the conditions under which such wasted management effort may occur. Introduced in approximately 1940, the fire ant spread widely through the southeast US and became a problematic pest. Historically, fire ants were managed with broad‐spectrum pesticides; unfortunately, these efforts were largely unsuccessful. One hypothesis suggests that, by also killing native ants, mass pesticide application reduced competitive burdens thereby enabling fire ants to invade more quickly than they would in the absence of management. We use a mechanistic competition model to demonstrate the landscape‐level effects of such management. We explicitly model the extent and location of pesticide applications, showing that the same pesticide application can have a positive, neutral, or negative effect on the progress of an invasion, depending on where it is applied on the landscape with respect to the invasion front. When designing management, the target species is often considered alone; however, this work suggests that leveraging existing biotic interactions, specifically competition with native species, can increase the efficacy of management. Our model not only highlights the potential unintended consequences of ignoring biotic interactions, but also provides a framework for developing spatially explicit management strategies that take advantage of these biotic interactions to work smarter, not harder. [ABSTRACT FROM AUTHOR]

Nonstandard numerical approximation for the study of a competition model for two species that experience nonlocal diffusion, or dispersion, allows for faithful representation of the theoretical solution to the system. Such a scheme may preserve positivity of solutions, be uniquely solvable, and be completely stable. Under appropriate conditions, the error between the scheme and the theoretical solution can be measured. We present such a scheme here and confirm its desirable properties as they reflect the solution to the system.

This paper proposed a stochastic toxin-dependent competition model to investigate the impact of environmental noise on species interaction dynamics. First, a survival analysis was conducted to establish the sufficient conditions for population extinction and persistence. Second, we proved the existence of a unique ergodic stationary distribution. Finally, the spatial arrangement of random states near the deterministic attractor was investigated using the stochastic sensitivity functions technique. This analytical approach facilitates constructing confidence ellipses and estimating critical noise intensity corresponding to the onset of transition. Both theoretical and numerical findings demonstrated that significant levels of noise experienced by one species lead to its extinction while promoting persistence in its competitor; conversely, negligible levels of noise did not alter the original competition outcomes in the deterministic model. However, when both species encounter moderate levels of noise, various modifications can occur in competition outcomes. These findings have significant implications for preserving ecosystem diversity.

Nonstandard numerical approximation for the study of a competition model for two species that experience nonlocal diffusion, or dispersion, allows for faithful representation of the theoretical solution to the system. Such a scheme may preserve positivity of solutions, be uniquely solvable, and be completely stable. Under appropriate conditions, the error between the scheme and the theoretical solution can be measured. We present such a scheme here and confirm its desirable properties as they reflect the solution to the system. [ABSTRACT FROM AUTHOR]

One of the shortcomings of the classical Lotka-Volterra competition model is that both species' births are assumed to be instantaneous, whereas developmental and maturation processes may cause time delays. We extend the Lotka-Volterra competition model to a delayed model based on a single species delayed model in this paper. The effects of two discrete delays on competition outcomes are investigated. Our theoretical and numerical results show that delays can cause the loss of stability of equilibria and the emergence of periodic solutions (i.e., population density oscillations) via Hopf bifurcation, lead to exclusion by changing the stability of coexistence equilibrium, and boost coexistence even if the coexistence equilibrium point does not exist. [ABSTRACT FROM AUTHOR]

Since the emergence of a transmissible cancer, devil facial tumour disease (DFT1), in the 1980s, wild Tasmanian devil populations have been in decline. In 2016, a second, independently evolved transmissible cancer (DFT2) was discovered raising concerns for survival of the host species. Here, we applied experimental and modelling frameworks to examine competition dynamics between the two transmissible cancers in vitro. Using representative cell lines for DFT1 and DFT2, we have found that in monoculture, DFT2 grows twice as fast as DFT1 but reaches lower maximum cell densities. Using co‐cultures, we demonstrate that DFT2 outcompetes DFT1: the number of DFT1 cells decreasing over time, never reaching exponential growth. This phenomenon could not be replicated when cells were grown separated by a semi‐permeable membrane, consistent with exertion of mechanical stress on DFT1 cells by DFT2. A logistic model and a Lotka–Volterra competition model were used to interrogate monoculture and co‐culture growth curves, respectively, suggesting DFT2 is a better competitor than DFT1, but also showing that competition outcomes might depend on the initial number of cells, at least in the laboratory. We provide theories how the in vitro results could be translated to observations in the wild and propose that these results may indicate that although DFT2 is currently in a smaller geographic area than DFT1, it could have the potential to outcompete DFT1. Furthermore, we provide a framework for improving the parameterization of epidemiological models applied to these cancer lineages, which will inform future disease management. [ABSTRACT FROM AUTHOR]

Stochastically perturbed models, where the white noise type stochastic perturbations are proportional to the current system state, the most realistically describe real-life biosystems. However, such models essentially have no equilibrium states apart from one at the origin. This feature makes analysis of such models extremely difficult. Probably, the best result that can be found for such models is finding of accurate estimations of a region in the model phase space that serves as an attractor for model trajectories. In this paper, we consider a classical stochastically perturbed Lotka–Volterra model of competing or symbiotic populations, where the white noise type perturbations are proportional to the current system state. Using the direct Lyapunov method in a combination with a recently developed technique, we establish global asymptotic properties of this model. In order to do this, we, firstly, construct a Lyapunov function that is applicable to the both competing (and globally stable) and symbiotic deterministic Lotka–Volterra models. Then, applying this Lyapunov function to the stochastically perturbed model, we show that solutions with positive initial conditions converge to a certain compact region in the model phase space and oscillate around this region thereafter. The direct Lyapunov method allows to find estimates for this region. We also show that if the magnitude of the noise exceeds a certain critical level, then some or all species extinct via process of the stochastic stabilization ('stabilization by noise'). The approach applied in this paper allows to obtain necessary conditions for the extinction. Sufficient conditions for the extinction (that for this model occurs via the process that is known as the 'stochastic stabilization', or the 'stabilization by noise') are found applying the Khasminskii-type Lyapunov functions. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Incentives are quite common to be utilized in engineering applications such as some infrastructure development projects or construction projects. Due to the increasing complexity of construction management and the continuing trend towards outsourcing of component or engineering outsourcing activities, we focus on the issue of incentive design. Time collaboration is one of the main focuses of random project duration time in parallel projects. In this article, we consider a setting where a manufacturer outsources two parallel subtasks to two different suppliers, and the manufacturer is time sensitive. On the premise that the project completion time follows the exponential distribution, some models are established to compare the proposed incentives and we get the comparative analysis of the proposed incentives. This paper puts forward three kinds of time-based incentive mechanisms, namely, deadline incentive mechanism, competition mechanism and mixed incentive mechanism. We do modeling analysis for all incentive mechanisms. We get the optimal work rates determined by suppliers and compare various incentive mechanisms to maximize manufacturers' profits. [ABSTRACT FROM AUTHOR]

This research probed how classifiers marking an object's membership in the grammar of classifier languages like Mandarin Chinese and Korean may influence their speakers to categorize objects differently compared to speakers of non-classifier languages like English. Surveys in multiple-choice format were given to native speakers of the three languages. Analysis of the results demonstrated that significant proportions of Mandarin Chinese and Korean speakers behaved differently from English speakers due to the classifier-based strategy influencing classifier language speakers' categorization. Adopting the Competition Model, we suggest that among the various categorizing strategies available to language users, the one with the greatest strength at the moment of performing the task wins the categorization competition. Classifiers that are grammaticalized in classifier languages may be providing their speakers with a powerful cognitive tool to notice diverse characteristics shared between objects, which is usually unavailable to non-classifier languages. Therefore, the strength of classifier-based strategy in the minds of classifier language speakers is strong enough to win some of the categorization competitions, which guides them to make different categorizing decisions from non-classifier language users. [ABSTRACT FROM AUTHOR]

This paper studies the Lotka-Volterra competition model with cross-diffusion terms under homogeneous Dirichlet boundary conditions. We consider the asymptotic behavior of positive steady-states as equal two cross-diffusion coefficients tend to infinity (so-called the full cross-diffusion limit). The first result shows that, at the full cross-diffusion limit, the set of positive steady-state solutions can be classified into two types: the small coexistence or the complete segregation. The small coexistence can be characterized by the set of positive solutions of a nonlinear elliptic equation, while the complete segregation can be characterized by the set of nodal solutions of another nonlinear elliptic equation. The second result concerns the global bifurcation structure of the 1d model with large cross-diffusion terms to show that the branch of small coexistence bifurcates from the trivial solution and many branches of complete segregation bifurcate from solutions on the branch of small coexistence. Finally, in order to verify the theoretical results, we chase some bifurcation branches numerically via the continuation software pde2path. [ABSTRACT FROM AUTHOR]

Abstract Since the emergence of a transmissible cancer, devil facial tumour disease (DFT1), in the 1980s, wild Tasmanian devil populations have been in decline. In 2016, a second, independently evolved transmissible cancer (DFT2) was discovered raising concerns for survival of the host species. Here, we applied experimental and modelling frameworks to examine competition dynamics between the two transmissible cancers in vitro. Using representative cell lines for DFT1 and DFT2, we have found that in monoculture, DFT2 grows twice as fast as DFT1 but reaches lower maximum cell densities. Using co‐cultures, we demonstrate that DFT2 outcompetes DFT1: the number of DFT1 cells decreasing over time, never reaching exponential growth. This phenomenon could not be replicated when cells were grown separated by a semi‐permeable membrane, consistent with exertion of mechanical stress on DFT1 cells by DFT2. A logistic model and a Lotka–Volterra competition model were used to interrogate monoculture and co‐culture growth curves, respectively, suggesting DFT2 is a better competitor than DFT1, but also showing that competition outcomes might depend on the initial number of cells, at least in the laboratory. We provide theories how the in vitro results could be translated to observations in the wild and propose that these results may indicate that although DFT2 is currently in a smaller geographic area than DFT1, it could have the potential to outcompete DFT1. Furthermore, we provide a framework for improving the parameterization of epidemiological models applied to these cancer lineages, which will inform future disease management.

The dynamics of two-plant competitive models have been widely studied, while the effect of chemical heterogeneity on competitive plants is rarely explored. In this study, a model that explicitly incorporates light and total phosphorus in the system is formulated to characterize the impacts of limited carbon and phosphorus on the dynamics of the two-plant competition system. The dissipativity, existence and stability of boundary equilibria and coexistence equilibrium are proved, when the two plants compete for light equally. Our simulations indicate that, with equal competition for light ($ b_{12} = b_{21} $) and a fixed total phosphorus in the system ($ T $), plants can coexist with moderate light intensity ($ K $). A higher $ K $ tends to favor the plant with a lower phosphorus loss rate ($ d_1 $ vs $ d_2 $). When $ K $ is held constant, a moderate level of $ T $ leads to the dominance of the plant with a lower phosphorus loss rate ($ d_1 $ vs $ d_2 $). At high $ T $ levels, both plants can coexist. Moreover, our numerical analysis also shows that, when the competition for light is not equal, the low level of total phosphorus in the system may lead the model to be unstable and have more types of bistability compared with the two-dimensional Lotka-Volterra competition model.

In this paper we consider a free boundary problem for a nonlocal time-periodic competition model. One species is assumed to adopt nonlocal dispersal, and the other one adopts mixed dispersal, which is a combination of both random dispersal and nonlocal dispersal. We first prove the global well-posedness of solutions to the free boundary problem with more general growth functions, and then discuss the spreading and vanishing phenomena. Moreover, under the weak competition condition, we study the long-time behaviors of solutions for the spreading case.

Language is a unique phenomenon and special enough to be treated meticulously in its analysis. Several models describe the underlying mechanisms for language acquisition and its processing. One of the most salient ones is the Competition Model suggested by Bates and MacWhinney (1982). We reviewed the CM from its initial principles proposed by Bates and MacWhinney, its adequacy and development, to its recent language learning version. This review discusses challenges regarding CM’s accountability for Persian and Bandari (a language variety of Persian) and its potential pedagogical implications. Conclusions are drawn on whether the CM can be implemented in first-language acquisition studies and second-language learning.

Population ecology theory is replete with density-dependent processes. However, trait-mediated or behavioral indirect interactions can both reinforce or oppose density-dependent effects. This paper presents the first two species competitive ODE and PDE systems, where the non-consumptive behavioral fear effect and the Allee effect, a density-dependent process, are both present. The stability of the equilibria is discussed analytically using the qualitative theory of ordinary differential equations. It is found that the Allee effect and the fear effect change the extinction dynamics of the system and the number of positive equilibrium points, but they do not affect the stability of the positive equilibria. We also observe standard co-dimension one bifurcation in the system by varying the Allee or fear parameter. Interestingly, we find that the Allee effect working in conjunction with the fear effect can bring about several dynamical changes to the system with only fear. There are three parametric regimes of interest in the fear parameter. For small and intermediate amounts of fear, the Allee + fear effect opposes dynamics driven by the fear effect. However, for large amounts of fear the Allee + fear effect reinforces the dynamics driven by the fear effect. The analysis of the corresponding spatially explicit model is also presented. To this end, the comparison principle for parabolic PDE is used. The conclusions of this paper have strong implications for conservation biology, biological control as well as the preservation of biodiversity. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to investigate the existence of positive solutions of a competition model with nonlocal diffusion and nonhomogeneous harvesting. Comparison arguments and sub‐super solutions method play a significant role in our main proof. [ABSTRACT FROM AUTHOR]

A diffusion-advection competition model with different pulses has been investigated in order to understand how the impulsive intervention affects the dynamics and alters the competition state of two competitors in open advective environments. The threshold values are introduced as the principal eigenvalues of the periodic problems with pulses and defined by the spectral radius of a time- T map. We have obtained two critical advection curves depending on pulses that determine the stability of the periodic steady states and have computed these numerically. The dynamics of two competitors in open advective environments such as competition exclusion, co-extinction, coexistence and bistability have been classified. By applying different impulsive effects, simulation analysis shows interesting scenarios, and reveals that a tradeoff between two different impulsive interventions and movements can be found in order to improve sustainable ecological development and economic benefits. [ABSTRACT FROM AUTHOR]

Ambiguous sensory information can lead to spontaneous alternations between perceptual states, recently shown to extend to tactile perception. The authors recently proposed a simplified form of tactile rivalry which evokes two competing percepts for a fixed difference in input amplitudes across antiphase, pulsatile stimulation of the left and right fingers. This study addresses the need for a tactile rivalry model that captures the dynamics of perceptual alternations and that incorporates the structure of the somatosensory system. The model features hierarchical processing with two stages. The first and the second stages of model could be located at the secondary somatosensory cortex (area S2), or in higher areas driven by S2. The model captures dynamical features specific to the tactile rivalry percepts and produces general characteristics of perceptual rivalry: input strength dependence of dominance times (Levelt's proposition II), short-tailed skewness of dominance time distributions and the ratio of distribution moments. The presented modelling work leads to experimentally testable predictions. The same hierarchical model could generalise to account for percept formation, competition and alternations for bistable stimuli that involve pulsatile inputs from the visual and auditory domains. [ABSTRACT FROM AUTHOR]

We investigate a class of partially degenerate nonlocal diffusion Lotka-Volterra competition models with a free boundary and a fixed boundary in which invasive species with nonlocal diffusion and native species without diffusion or very slow diffusion. We first prove the existence and uniqueness of the global solution. Then we consider the long-time behavior of the solution when the invasive species are inferior and superior, respectively. Finally, criteria of spreading and vanishing are established when u is the superior competitor. [ABSTRACT FROM AUTHOR]

The objective of the study was to describe circular economic engineering by means of a systematic analysis from open science. The study was conducted in October 2023. Using the ScienceDirect database, the following search equation with Boolean signs was entered: "circular economy model" AND "technological innovation" AND "development". The years 2021, 2022 and 2023 were filtered. The selected articles corresponded to the type of review with open access. The information was analyzed using the PRISMA methodology. Thirty-two articles were identified and four were finally analyzed, corresponding to 2022 and 2023. The CE based on technological innovation considers, a traceability that starts with a management thinking of eco-efficient processes through sanitation and use of treated resources, distribution of marked use, consumption and optimal deposit and recycling. After 2018 none of the four articles showed matching referential citations. It is concluded, that CE is described from a variety of analyses that enable efficient and sustainable use of resources. [ABSTRACT FROM AUTHOR]

We study a two-species competition model in a patchy advective environment, where the species are subject to both directional drift and undirectional random dispersal between patches and there are losses of individuals in the downstream end (e.g., due to the flow into a lake or ocean). The two competing species are assumed to have the same growth rates but different advection and random dispersal rates. We focus our studies on the properties of an associated eigenvalue problem which characterizes the extinction/persistence dynamics of the underlying patch population model. We also derive conditions on the advection and random dispersal rates under which a mutant species can or cannot invade the resident species. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of bistable pulsating wave for a two-species competition system in rapidly periodically varying media and its homogenization limit as the spatial period tends to zero. Assuming that the homogenized system admits a bistable traveling wave, we first show the existence of pulsating wave for all small periods and determine the homogenization limit of the wave speed. Furthermore, in the case where the homogeneous wave is not stationary, we investigate the effects of spatial heterogeneity on the wave speeds. Our estimates indicate that the deviation of the wave speeds in comparison to the homogeneous one is at most linearly along with small period in the general case, and is of second order where the heterogeneity appears only in the diffusion coefficients. [ABSTRACT FROM AUTHOR]

A good pricing strategy is a key factor in the success of a company's products. However, fierce competition and an ever-increasing number of market players are forcing companies to use automated methods and systems to respond in real time to changes in customer purchasing power and competitors' marketing techniques. More importantly, multi-agent modeling tools are used to select the most successful pricing strategy in the first place and consider all factors influencing the final decision. This paper presents a possible variant of a multi-agent model for determining the optimal pricing policy of a company. The results show that the limited rationality and interaction of each agent determines the unique behavior of the system and that the pricing strategy affects the profit and market share of the firm. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we have studied a three-dimensional model to describe the behavior of tumor cells in the absence of the immune response, which is composed of tumor, normal and fat cells (TNF) under time delay effect. The center manifold theory has been used to study the bifurcation behavior. It is proven that TNF model undergoes codimension-1 bifurcation, while Hopf bifurcation does not occur in the non-delay model. For delayed TNF, we take into the late response of fat cells to tumor cells. Consequently, the delay factor is a considerable parameter in TNF model. Hence, we presented a formula of the time delay value for the occurrence of periodic solutions. Additionally, the stability of Hopf bifurcation was analysed. Numerical simulations are provided to illustrate and extend the theoretical results, we provide our study with numerical simulations inclusive families of periodic solutions.

In the search for causes and cures of cancer diseases, many mathematical models developed have resulted in systems of nonlinear stiff ordinary differential equations. With these models, many numerical estimates of biological knowledge of the parameters have been obtained, a number of phenomena interpreted, and predictions were made in order to gain further knowledge of cancer development and possible treatment. In this study, numerical simulations of the models were performed using continuous block implicit hybrid methods and the results obtained support the theoretical and clinical findings. We analyzed the interactions among the various tumor cell populations and present the results graphically. From the graphical representation of results, one can clearly see the effects of all the tumor cell populations involved in the competition, as well as the effects of some treatments by the applications of some therapeutic agents which have been heavily used in the clinical treatments of breast cancer. The treatments in the past were mostly conventional chemotherapies, which were used either singly (alone) or in combination with each other or other therapies, and all played vital roles, except for the side effects that these therapies incur in normal tissues and organs. Thus, from recent research works, it is now clear that in many cases they do not represent a complete cure. Therefore, the need to address not only the preventative measures of breast cancer, but also more successful treatment, is clear, and can be successfully achieved to increase the survival rate of breast cancer patients. [ABSTRACT FROM AUTHOR]

Two or more consumer species compete for a same source in a competitive model, The amount of a limiting resource in the environment reduces when two or more species compete for it, These species also confront other threats for their survival, such as health concerns, infection, pollution, and so on, Based on above, in this paper we develop a competition model where we have consider two logistically growing species competing for the same resource, Also, there is infection in one of the species, We study the influence of disease and pollutants on the competing population with delay in the transmission of infection in infective class, The characteristics of the model has been discussed to prove that the described system is bounded, The existence of infection-free equilibrium point and endemic equilibrium point of the system has been shown, in case of coexistence of the species, The stability analysis of the equilibrium points has been examined using the Routh-Hui twiz criteria, The occurrence of hopf bifurcation considering time lag (15) as a critical parameter has been examined, The direction and stability of hopf bifurcation has been investigated, Numerical simulations have been performed using MATLAB to prove our analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we have studied a three-dimensional model to describe the behavior of tumor cells in the absence of the immune response, which is composed of tumor, normal and fat cells (TNF) under time delay effect. The center manifold theory has been used to study the bifurcation behavior. It is proven that TNF model undergoes codimension-1 bifurcation, while Hopf bifurcation does not occur in the non-delay model. For delayed TNF, we take into the late response of fat cells to tumor cells. Consequently, the delay factor is a considerable parameter in TNF model. Hence, we presented a formula of the time delay value for the occurrence of periodic solutions. Additionally, the stability of Hopf bifurcation was analysed. Numerical simulations are provided to illustrate and extend the theoretical results, we provide our study with numerical simulations inclusive families of periodic solutions. [ABSTRACT FROM AUTHOR]

In this paper we give a classification of the global asymptotic stability for a nonlocal diffusion competition model with free boundaries consisting of an invasive species with density u and a native species with density v. We not only prove that such nonlocal diffusion problem has a unique global solution and also determine the long-time asymptotic behavior of the solution for three competition cases : (I) u is an inferior competitor, (II) u is a superior competitor and (III) the weak competition case. Especially, in case (II), under some additional conditions, we determine the long-time asymptotic behavior of the solution when vanishing happens. Moreover, the criteria for spreading and vanishing are obtained. [ABSTRACT FROM AUTHOR]

The objective of our study is to capture the roles of product quality and network effects in the success and efficiency of network markets under strategic settings that defined in terms of market share as a strategic factor and profit as a financial indicator. The research paper shows that the efficiency of network markets depends heavily on the phase adjustment of competition models and the balance of network effects and product quality among enterprises. the network market is always efficient in price competition, but not true in quantity competition when the network effect difference is sufficiently large or/and the quality difference is relatively small, then network effects may play a perverse role in market efficiency. The main findings reveal that network effects do not always enhance the role of quality in market efficiency and market growth. The research outcomes point to high quality enterprises' attitude toward compatibility with enterprises with large network effects. This research paper also offers insights on government intervention to correct the distorted impacts of sufficiently large network effects on the efficiency of network markets. [ABSTRACT FROM AUTHOR]

We study stability analysis of a discrete-time dynamical system of Wolbachia diffusion in mosquito populations with Allee effects on the wild mosquito population. We analyze the competition between released mosquitoes and wild mosquitos. We show local and global stabilities of the fixed points, and type of bifurcations concerning parameters. The results are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This study examines the role of cross-linguistic transfer versus general processing strategy in two groups of heritage speakers (n = 28 per group) with the same heritage language – Russian – and typologically different dominant languages: English and Estonian. A group of homeland Russian speakers (n = 36) is tested to provide baseline comparison. Within the framework of the Competition model (MacWhinney, 2012), cross-linguistic transfer is defined as reliance on the processing cue prevalent in the heritage speaker's dominant language (e.g. word order in English) for comprehension of heritage language. In accordance with the Isomorphic Mapping Hypothesis (O'Grady and Lee, 2005), the general processing strategy is defined in terms of isomorphism as a linear alignment between the order of the sentence constituents and the temporal sequence of events. Participants were asked to match pictures on the computer screen with auditorily presented sentences. Sentences included locative or instrumental constructions, in which two cues – word order (basic vs. inverted) and isomorphism mapping (isomorphic vs. nonisomorphic) – were fully crossed. The results revealed that (1) Russian native speakers are sensitive to isomorphism in sentence processing; (2) English-dominant heritage speakers experience dominant language transfer, as evidenced by their reliance primarily on the word order cue; (3) Estonian-dominant heritage speakers do not show significant effects of isomorphism or word order but experience significant processing costs in all conditions. [ABSTRACT FROM AUTHOR]

In this paper we study a free boundary problem of the diffusive competition model with different habitats. It is assumed that the habitats of the two species u and v are (- ∞ , g (t)) and (h (t) , ∞) , respectively, and g (0) < h (0) . In their separate habitats, the two species obey the diffusive logistic equations. In their common habitat, they are in competition. We investigate the existence, uniqueness, regularity, uniform estimates and long time behavior of the global solution. Some sufficient conditions for the spreading and vanishing are also established. [ABSTRACT FROM AUTHOR]

In the present study, we aimed to demonstrate that allelopathic compounds from the cyanobacterium Phormidium sp. can induce the collapse of large populations of the cyanobacteria Microcystis aeruginosa Kützing Kützing. We employed several strains of this toxic cyanobacteria, from six different locations, in order to test for adaptive variation in resistance to allelochemicals. As a preliminary test to detect allelopathic effect, we performed bioassays with Phormidium allelochemicals against the different strains of M. aeruginosa at low population abundances. Then, we combined long-term competition experiments and mechanistic modelling with two purposes: (a) demonstrate that the inhibitory effect of Phormidium sp. against M. aeruginosa was due to allelopathy and not resource competition; (b) test the effectiveness of these allelochemicals at inducing the collapse of large populations of M. aeruginosa. Our results showed a strong allelopathic effect of Phormidium, which induced the collapse of large populations of M. aeruginosa, without evidence of differences in sensitivity between strains. We demonstrated that allelopathy (interference competition) can reverse the outcome predicted by resource competition (exploitation competition). These results are encouraging in order to take further steps in the development of a bioremediation method, based in Phormidium allelopathy, against blooms of toxic cyanobacteria. [ABSTRACT FROM AUTHOR]

Breast cancer is a complex disease with significant phenotypic heterogeneity of cells, even within a single breast tumor. Emerging evidence underscores the significance of intratumoral competition, which can serve as a key contributor to cancer drug resistance, imparting substantial clinical implications. Understanding the competitive dynamics is paramount as it can significantly influence disease progression and treatment outcomes. In the present work, a mathematical model was developed using a system of differential equations to describe the dynamic interactions between two cancer subtypes (each further classified into cancer stem cells and tumor cells) and innate immune cells. The purpose of the model is to comprehensively understand the competitive interactions between the heterogeneous subpopulations. The equilibrium points and stability analysis for each equilibrium point were established. Model simulations showed that the competition between two cancer subtypes directly affects the number of both species. When competition between two cancer subtypes is strong, increasing the immune response rate specific to the more competitive species effectively reduces the tumor size. However, if the competition is relatively weak, an optimal immune response rate is required to minimize the total number of tumor cells. Rates below the optimal level fail to reduce the population of the stronger species, whereas rates above the optimal level can lead to the recurrence of the weaker species. Overall, this model provides insights into breast cancer dynamics and guides the development of effective treatment strategies.

In this paper, the positive solutions of a diffusive two competitive species model with Bazykin functional response are investigated. We give the a priori estimates and compute the fixed point indices of trivial and semi-trivial solutions. And obtain the existence of solution and demonstrate the bifurcation of a coexistence state emanating from semi-trivial solutions. Finally, multiplicity and stability results are presented. [ABSTRACT FROM AUTHOR]

Goal: This study aims to explore the relationship between companies leveraged by the use of 5G technologies and Industry 4.0 to develop a model that explains the impacts on the ecosystem. Design / Methodology / Approach: This study applies a bibliometric research utilizing scientometric review to provide an understanding of the status quo and the trend for research on the tripod theme in the world: (a) Firm Network, (b) Industry 4.0 and (c) 5G Technology. The study is extended by a qualitative research applying critical incident technique to experts´ interviews looking for the gap in the bibliometric review and insights on the tripod theme to develop a Conceptual Model based on grounded theory. Results: A conceptual model of balanced competitive expansion of the market was developed regarding the bibliometric and qualitative research. The model, based on 5 hypotheses - related to Partnership, Competition and Products and Services – highlights that while the 5G technology and Industry 4.0 impact the relationship among companies (competition, partnerships, product and services) this impact is balanced with a market expansion. Limitations of the investigation: This proposed conceptual model must be evaluated with quantitative research to validate the variables and hypothesis developed based on grounded theory. Practical implications: This paper shows methodological steps and basis to develop a conceptual model to be validate with broadly quantitative survey. Originality / Value: The paper demonstrates its originality and relevance by presenting a model relating innovative technology trends and their impact in the ecosystem